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A New Algebraic Geometry Algorithm for Integer Programming


  • Dimitris Bertsimas

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Georgia Perakis

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Sridhar Tayur

    (Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)


We propose a new algorithm for solving integer programming (IP) problems that is based on ideas from algebraic geometry. The method provides a natural generalization of the Farkas lemma for IP, leads to a way of performing sensitivity analysis, offers a systematic enumeration of all feasible solutions, and gives structural information of the feasible set of a given IP. We provide several examples that offer insights on the algorithm and its properties.

Suggested Citation

  • Dimitris Bertsimas & Georgia Perakis & Sridhar Tayur, 2000. "A New Algebraic Geometry Algorithm for Integer Programming," Management Science, INFORMS, vol. 46(7), pages 999-1008, July.
  • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:7:p:999-1008

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    References listed on IDEAS

    1. Lawrence M. Leemis, 1991. "Nonparametric Estimation of the Cumulative Intensity Function for a Nonhomogeneous Poisson Process," Management Science, INFORMS, vol. 37(7), pages 886-900, July.
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    Cited by:

    1. Castro, F. & Gago, J. & Hartillo, I. & Puerto, J. & Ucha, J.M., 2011. "An algebraic approach to integer portfolio problems," European Journal of Operational Research, Elsevier, vol. 210(3), pages 647-659, May.


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